1. Technical Field
The disclosure is related generally to a controller system. More particularly, the disclosure is related to a controller system for a variable parameter and a related program product.
2. Related Art
Most control problems involve the design and/or synthesis of a controller system that is robust to process uncertainty. Process control applications often pose the additional challenge of custom installations where the level and type of uncertainty are not only driven by (uncontrolled) manufacturing variability, but are often imposed by design changes implemented to fit a customer's specific requirements. Most of the time field engineers (who may or may not have a background in feedback control systems) are required to tune controller systems in the field. Typically, the controllers selected for field tuning are of the PID variety (Proportional+Integral+Derivative) as the tuning for PID controllers are relatively more straightforward, better understood, and well-established, but still very challenging to manage.
The primary limitation of PID controllers is the lack of robustness to unmodeled dynamics. As PID controllers are linear and utilize fixed parameters, the closed loop performance of a PID-controlled system is sensitive to unmodeled process dynamics. For example, as shown in FIG. 1, a conventional PID controller may control a variable parameter, such that over a period of time, the actual parameter value (x) is substantially identical to the target values (xm) of the variable parameter. However, as shown in FIG. 1, in response to a disturbance, such as the indicated initial start of the process or a significant change (e.g., stepdown) in the target value, the process utilizing the PID controller may take a significant, undesirable amount of time to reach the target value. The time it takes to reach the target value is strongly dependent on the overall process dynamics and any unmodeled aspects of the process dynamics may result in slower system response or in a closed loop unstable system.
This sensitivity to unmodeled dynamics can lead to several challenges. In cases where one set of controller parameters is used for a large number of units (i.e., mass production) unit-to-unit variability can significantly challenge the overall capability of PID controllers. In cases where individual units are custom-designed it is often possible to calibrate individual units and combat unit-to-unit variability challenges, however, these individual tuning exercises are often costly and effectiveness of the resulting calibrations is highly variable due to the varying background of field engineers.
Another example of a conventional controller system may include a self-oscillating adaptive controller. A block diagram for a standard self-oscillating adaptive (SOA) controller 10 is shown in FIG. 2. An SOA controller 10 typically includes a linear compensator 12 (and perhaps a second filter (not shown) for the primary forward loop)), a relay 14 in the primary forward loop, and a gain changer subsystem 30 to modify the gain of the relay. A process 20 at issue has a variable parameter x responsive to a command or correction signal u that ideally follows a target value xm provided by a reference model 22. Linear compensator 12 can be constructed in any necessary form as established in the literature (e.g., using a linear low-order filter or the use of a process model representing the entitlement capability of the closed loop system). For example, linear compensator 12 (Gf(s)) may include a lead compensation filter and can be utilized to set the frequency of limit cycles (i.e., the oscillations or “chatter” that the relay will cause at steady-state). Gain changer subsystem 30 typically includes a low-pass filter 32 followed by a nonlinear, gain changer function 34 to determine the size of the gain for different operating conditions. The primary purpose of gain changer function 34 is to slowly alter the gain so that the system can have high gain levels that provide the robustness under transient conditions (characterized by large filtered error values), while lowering the gain of relay 14 under steady-state conditions (characterized by low filtered error values). As illustrated by comparing FIG. 3 to FIG. 1, SOA controller 10 may more quickly move the actual variable parameter value x of process 20 toward target value xm during unmodeled dynamics, e.g., an initial start of the process or during a significant change in the desired value. However, as shown in FIG. 3, SOA controller 10 output may continuously oscillate within a fairly large range both above and below target value xm. As a result, while SOA controller 10 may allow the process to operate closer to target value xm quickly, the large fluctuation in values is not ideal.
Most existing control algorithms that are capable of providing robust closed loop response are of moderate to high complexity. The synthesis of such systems may require detailed theoretical analysis as well as an in-depth understanding of the process dynamics. This additional complexity is often the driving factor for the selection of PID controllers for many practical feedback control applications despite their stated limitations.